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[fitsbits] CDELTn



 
 
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  #1  
Old September 20th 07, 05:57 AM posted to sci.astro.fits
Mark Calabretta
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Default [fitsbits] CDELTn


On Wed 2007/09/19 10:30:04 +0200, Francois Ochsenbein wrote
in a message to:

... I always understood that the coordinate value is
CRVALn + (i-CRPIXn)*CDELTn

which simply means that the value of the coordinate along this axis
is constant and equal to CRVALn, which seems to me perfectly correct
(a 1-point dimension is by definition a constant).


Francois,

It's perfectly illegal, Sect. 2.1.2 of WCS Paper I leaves no room for
doubt:

"The PCi_j matrix must not be singular; it must have an inverse.
Furthermore, all CDELTi must be non-zero. In other words,
invertibility means that transformations which project from an
initial coordinate system of dimensionality WCSAXES to a world
coordinate syetem of dimensionality less than WCSAXES are
forbidden."

Why bother spending 10 years agreeing on a standard if people feel they
can flout it in such a trivial and pointless way? To reiterate:

1) The coordinate transformation must be invertible. In particular,
CRVALia must be non-zero and the PCi_ja (or CDi_ja) matrix must not
be singular.

2) There is no connection between the image WCS and NAXISn - the WCS
doesn't know and doesn't care whether the image has degenerate axes.
NAXISn does not figure in the coordinate transformation equations,
not even for conventional types (COMPLEX, STOKES, CUBEFACE), and is
rarely even mentioned in any of the WCS papers.

3) If CDELTia isn't meaningful, as for a degenerate axis, then simply
omit it. It defaults to 1.0.

Mark Calabretta

  #2  
Old September 20th 07, 09:04 AM posted to sci.astro.fits
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Default [fitsbits] CDELTn

On Thu, 20 Sep 2007, Mark Calabretta wrote:

It's perfectly illegal, Sect. 2.1.2 of WCS Paper I leaves no room for
doubt:

"The PCi_j matrix must not be singular; it must have an inverse.
Furthermore, all CDELTi must be non-zero. In other words,


To repeat what I said in a previous post, WCS papers will be
"incorporated by reference" in the draft FITS standard 3.0, so there
will be no doubt they are applicable. But maybe it is worth adding
ranges of legal values to table 8.2 of thereabout (Bill are you keeping
track of this for when you return from the ADASS ?)

The only other point is that CDELTn were around before WCS, and we have
in 3.0 the rule that a change of a standard cannot make invalid what
done before ...

3) If CDELTia isn't meaningful, as for a degenerate axis, then simply
omit it. It defaults to 1.0.


Looks a sensible suggestion. Not using degenerate axes is perhaps even
more sensibile :-)

Lucio Chiappetti

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  #3  
Old September 20th 07, 08:01 PM posted to sci.astro.fits
Thierry Forveille[_2_]
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Default [fitsbits] CDELTn

The only other point is that CDELTn were around before WCS,
Around before the WCS paper yes, but not around before WCS: a
minor source of confusion in this discussion has been that WCS
existed from the very begining of FITS (the WCS phrase may have
appeared later, not really sure, but the concept was there from
the begining), in their basic linear and orthogonal form. What
the WCS paper did was add support for distortion, projections,
but basic WCS is much older.

3) If CDELTia isn't meaningful, as for a degenerate axis, then simply
omit it. It defaults to 1.0.


Looks a sensible suggestion. Not using degenerate axes is perhaps even
more sensibile :-)

Not at all :-) Degenerate axes are actually a most natural (if perhaps
initially slightly counterintuitive, for some) way of conveying position
information along the missing axes. One classical example is using
two degenerate axes to convey RA & Dec (or lII & bII, or whatever)
information for a set of individual spectra obtained on a grid,
where you can set CDELTn to the grid spacing, CRVALn to RA at grid
center, and CRREFn to the pixel position of the grid center relative
to current datum (i.e. minus the pixel position of current datum
in the grid). Very convenient, and commonly used for single-dish
radioastronomical spectra.
  #4  
Old September 21st 07, 03:42 AM posted to sci.astro.fits
Doug Tody
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Default [fitsbits] CDELTn

On Thu, 20 Sep 2007, Thierry Forveille wrote:

Looks a sensible suggestion. Not using degenerate axes is perhaps even
more sensibile :-)

Not at all :-) Degenerate axes are actually a most natural (if perhaps
initially slightly counterintuitive, for some) way of conveying position
information along the missing axes.


This has long been a point of argument. In one view a dataset can
be viewed as N-dimensional, where N is large and there can be many
"axes", any of which are potentially degenerate (single valued).
In the other view, one has an N-dimensional sampled dataset and any
number of other dataset attributes which are constant for the entire
dataset but which do not qualify as sampled axes.

The degenerate axis view might make sense for a very few things which
are often sampled (polarization, frequency/velocity, possibly time),
where a common model can be used whether or not a given physical
"axis" is sampled (Characterization in VO is similar). But in the
general case, applied to any "image" attribute, this is a poor model.

- Doug
  #5  
Old September 21st 07, 08:03 AM posted to sci.astro.fits
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Default [fitsbits] CDELTn

On Thu, 20 Sep 2007, Thierry Forveille wrote:

The only other point is that CDELTn were around before WCS,

Around before the WCS paper yes, but not around before WCS: [...]
but basic WCS is much older.


I was of course referring to the WCS papers. The "basics" (CRVAL CRPIX
CDELT and CROTA) were probably there since the very beginning (but CROTA
was later deprecated). I am not able now to verify if any of the
earliest (pre-WCS-paper) standards explicitly specified constraints for
CDELT ... and hence to tell whether Francois's CDELT=0 files were once
legal.


Looks a sensible suggestion. Not using degenerate axes is perhaps even
more sensibile :-)

Not at all :-) Degenerate axes are actually a most natural (if perhaps
initially slightly counterintuitive, for some) way of conveying position
information along the missing axes. One classical example is using
two degenerate axes to convey RA & Dec (or lII & bII, or whatever)
information for a set of individual spectra obtained on a grid,


I was thinking of much sillier cases. People writing a 1-d spectrum as a
FITS image (and this instead of a bintable is something I accept) as
NAXIS=2 NAXIS1=nbins NAXIS2=1


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